Journal of Symplectic Geometry

Volume 6 (2008)

Number 2

Holomorphic vector fields and perturbed extremal Kähler metrics

Pages: 127 – 138

DOI: http://dx.doi.org/10.4310/JSG.2008.v6.n2.a1

Author

Akito Futaki

Abstract

We prove a theorem which asserts that the Lie algebra of all holomorphic vector ﬁelds on a compact Kähler manifold with a perturbed extremal metric has the structure similar to the case of an unperturbed extremal Kähler metric proved by Calabi.